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Month: August 2020

Impact of external factors on shooting performance in biathlon

Posted on 2020-08-27 | by biathlonanalytics | Leave a Comment on Impact of external factors on shooting performance in biathlon

by
Puck Possessed

In the third issue of Puck Possessed Biathlon, I want to look at the influence of things like weather and snow conditions, as well as course information. This is all summarized in reports made available on the https://biathlonresults.com/ website as Final Results – Competition Data Summary:

From this report, I used the measurements provided, except for the measurement taken half an hour before the race, as it doesn’t seem that relevant. Also, all these measurements should be taken with a grain of salt (how accurately are they measured, it’s only on one measure location, and some “measurements” are qualitative. In addition I tried my best to find a general elevation for the biathlon stadiums using Google Earth, so that data quality is also limited. Lastly, working only with the data I have, I had to make some assumptions. I realize that a maximum climb right before the shooting range makes a course harder than when it is right after the stadium. I tried looking into course profiles, but they are surprisingly hard to get (in a useful format).

To make all this data a bit easier to work with, I created a number of categories or indexes based on similar/related measurements, rather than using all data individually:

Wind

  • Wind strength (using the maximum value of the Wind Direction/Speed row);
  • Wind direction variability (the maximum difference in degrees between the three measured wind directions;
  • Wind strength variability (difference between minimal and maximum).

Visibility

  • Weather description (qualitative) is typically the same during the race, with a few exceptions (two out of 25 at the time of writing). I grouped some values in categories as they are very similar related to visibility:
    • Clear sky & Sunny
    • Cloudy, Low-level cloud, Partly cloudy
    • Light rain, Light snow, Light snowfall and Rain
    • Heavy snow & Snow

Humidity

  • Humidity measurements.

Course

  • Total Course Length;
  • Height Difference;
  • Maximum Climb;
  • Total Climb;
  • Elevation;
  • Snow of the track.

Not included

  • Air Temperature. Even though it varies, I don’t see how this could have an impact on performance, especially since events get cancelled when the temperature drops below a value where it could impact shooting. Note that I am aware that temperature impacts the tracks, but I think that is better measured by using Snow temperature;
  • Humidity. I tried to find any correlation between humidity and shooting performance but was unable to, leading to the conclusion that humidity by itself has no impact on shooting performance. Of course humidity is related to precipitation, but that aspect is covered in the Weather section.

Now the question is how to measure shooting performance. The obvious measurement is the number of shots missed, but I don’t want to ignore shooting times. For example if athlete A has no misses but takes 30 seconds longer to shoot than athlete B who may have one miss, that still says something about shooting performance compared between athletes A and B. I also considered including range time, but I consider that to be more related to ski performance. So for this exercise I am using Shooting Times and Penalty Times (in seconds) as the latter are directly related to misses and allows for combining it with shooting speed.

Next step is indexing the different categories, starting with Wind. Let’s look first at the correlation between the different wind factors and shooting performance as described above:

This tells me that the biggest correlation (and most reliable) is the wind strength, and that both strength and direction variability are not significant:

Let’s dig a little deeper here. Although on it’s own the maximum wind speed may have the most (and only) impact, how about the combination of wind speed and speed variability and direction variability?

The following charts show there is actually a almost 70% correlation between wind strength variability and maximum strength (direction variability not at all):

So we’ll need to look at combinations of maximum wind speed and change in speed. Logically it makes sense too. Even if the wind changes direction, if the wind is not very strong it won’t have much of an impact. But variable wind speeds, especially whit some strong gusts are tough to adjust to).Now how about visibility? That becomes a bit more complicated, or less objective, as we don’t have measures for visibility, but rather subjective observations. Let’s look at the number of athletes with specific number of misses per race per season, and relate that to the weather description:

This gives me some indication of what are good shooting conditions, and which ones are less preferable. Let’s simplify this a bit more, by assuming a solid shooting performance is two misses or less; anything more and you are typically out of the race for gold (expect when you have exceptional ski speed):

Based on all this information (and knowingly ignoring other factors that contribute to these number), I’m going to state that Clear sky, Sunny, Cloudy, Light snowfall and Rain typically lead to solid shooting performances, with well over 70% of all athletes having 2 misses or less, whereas Partly cloudy, Snow, Heavy snow, Light rain, Light snow and Low-level cloud lead to lesser shooting performances. Partly cloudy, Light snow and Light rain appear to be the worst conditions.

That leaves us with the course conditions. And other than Total Climb in meters (which is still statistically insignificant with a p-value of 0.06) none of the course condition factors show any correlation to shooting performance (defined as shooting and penalty times), with p-values over 0.7 and R2-values lower than 0.005:

These charts look at event averages, but looking at individual athlete shooting performances the results are very similar:

Although it is hard to imagine course conditions having no indirect impact on shooting performance (many steep climbs, especially before entering the stadium, or wet, slow snow which makes the athletes work harder, etc.) I’m going to assume there is no direct impact on shooting performance. But that would be an interesting analysis for a future edition of Puck Possessed Biathlon for sure.

So in summary, we are going to index or score wind influence and visibility influence. And based on the information we gathered so far, I’m going to say that 

Weather

Clear sky, Sunny, Cloudy, Light snowfall and Rain = Good

Snow, Heavy snow and Low-level cloud = Medium

Partly cloudy, Light snow and Light rain = Bad

Wind

IF [WindStrengthMAX (copy)] >= 2 AND [WindStrengthDiff] >= 1.2 THEN "Bad"
ELSEIF [WindStrengthMAX (copy)] >= 2 AND [WindStrengthDiff] < 1.2 THEN "Medium"
ELSEIF [WindStrengthMAX (copy)] < 2 AND [WindStrengthDiff] >= 1.2 THEN "Medium"
ELSE "Good"
END

Now we can assign values to good, medium and bad (1, 2 and 3) and create a External Factor Index, that we can then try to measure up against the Shooting Performance indicator described earlier:

The green dots symbolize events in the 2017-2018 season, yellow 2018-2019 and grey the current season.

All in all a lot of work to come to the conclusion that there is a correlation between our defined Shooting Performance, and the External Factor Index, mostly based on wind and weather: the P-value is 0.0041 and thus significant, and the R2-value is 0.295. 

As I am sure you have figured out if you got this far, my statistical knowledge is limited. But I would say, that based on all assumptions made above, roughly 30% of shooting performance is impacted by weather conditions mentioned above.

Of course this research can use a lot of improvement. For example rather than comparing average shooting performances per event, look at standardized shooting performances. And the External Factor Index is based on a number of assumptions that are, to say the least, arbitrary. But the exercise was fun, and I believe I learned a lot more about the data of women’s biathlon sprint races.

If you have any feedback or comments, please reach out on Twitter: @rjweise

Posted in Statistical analysis | Tagged Puck Possessed, shooting

Importance of Skiing and Shooting in biathlon

Posted on 2020-08-27 | by real biathlon | 1 Comment on Importance of Skiing and Shooting in biathlon

The z-scores for last season’s basic statistics are a good tool to take a more theoretical look at biathlon. One of the things which always interests me on a general level is the question: what is more important, skiing or shooting?

The two charts show the z-scores for median ski speed and shooting efficiency (a.k.a. lost time at the range) for all 2013–14 World Cup starters (arranged by World Cup rank). The men’s and women’s chart is quite similar in how skiing and shooting seemingly influences the Overall World Cup rank. Generally, the performances get worse the farther down the rankings you go (as you would expect), however, it appears the higher ranked half of the World Cup field, on average, is better at skiing, while the bottom half are better shooters than skiers (per definition, negative values are good, positive values are bad here).


In order to quantify the effect that skiing and shooting has on an athlete’s World Cup rank, I came up with the idea to interpret the three sets of data – ski speed, shooting efficiency and World Cup rank – as a system of linear equations (all in z-scores). I don’t want to go into too much detail, but I explained it a bit more here before. 


Mathematically speaking, the system is overdetermined, i.e. there are more equations than unknowns, and inconsistent, i.e. it has no solution. However, using the method of least squares, you can find an approximate solution. The ratio between the least squares coefficients indicates the approximate influence of these elements (here the influence of skiing and shooting for the World Cup rank).

  Men Women
        Skiing       Shooting        Skiing     Shooting
Top 20 54.8 45.2 61.1 38.9
Top 40 57.9 42.1 56.3 43.8
Top 60 65.8 34.2 61.4 38.6
Top 100 61.2 38.8 65.2 34.8
All 66.1 33.9 66.2 33.8
average 61.2 38.8 62.0 38.0
Importance of Skiing and Shooting 
for Overall World Cup rank  (in %)  | 2013–14

For last season, all groups I looked at, both male and female, produced pretty consistent results. On average, skiing (61%-62%) was the more important factor for the World Cup rank than shooting (38%-39%). For both genders, skiing has the biggest influences if you look at where an athlete is ranked among the entire field; shooting gets slightly more important for smaller groups (most among the men’s top20 → 45%). However, the fewer athletes (i.e. linear equations) you take into account, the less robust and more random the results get. 

Taking it one step further, I split up general shooting into shooting accuracy and shooting speed (range time). This leads to a linear system with three unknowns (ski speed, shooting % and range time), and the influence of each category can again be approximated with the least squares coefficients’ ratio.

The results you get for three elements are very consistent with the results above: the influence of skiing for the World Cup rank is at about 60% (on average). The shooting accuracy is more important (about 25%) than the shooting pace (about 15%). Still, the range time is probably a lot more important than you would expect (especially compared to shooting percentage). Again the results for men and women are very similar. 

  Men Women
  Skiing Shooting %

Range Time

Skiing

Shooting%

Range Time
Top 20 52.0 30.5 17.5 59.2 25.1 15.7
Top 40 60.1 23.8 16.1 53.8 24.1 22.1
Top 60 67.7 23.6 8.7 57.4 21.0 21.5
Top 100   64.3 23.9 11.8 60.9 20.6 18.5
All 60.0 27.5 12.4 64.2 27.0 8.8
average 60.8 25.9 13.3 59.1 23.6 17.3
Importance of Skiing, Shooting % and Range Time 
for Overall World Cup rank  (in %)  |  2013–14

All of this is only a very imprecise approximation of course, based on a small sample size (no group is larger than 200 athletes). However, the fact that the results, which are highly theoretical, are quite similar across all groups and genders, might be an indication there is some merit to it. Also, using a sightly different method, I got results along the same lines in the past (then 65-35, now 60-40). Using z-scores should be methodologically more sound though.

The fact that shooting is equally important for men and women is actually surprising, because women must ski a longer penalty loop relative to their total course length. Shooting penalties should have a bigger effect in female competitions, however the larger skiing differences among women apparently compensates for that perfectly.

Posted in Statistical analysis | Tagged shooting, skiing

The Queen of Pursuit

Posted on 2020-08-27 | by biathlonanalytics | Leave a Comment on The Queen of Pursuit

by
Puck Possessed

I did research on Pursuit races of the 2019-2020 season to find out who the real Queen of Pursuit was for the last season. Here’s a summary of my findings:

Posted in Statistical analysis | Tagged Puck Possessed, pursuit

What’s more important, Shooting or Skiing?

Posted on 2020-08-25 | by real biathlon | 2 Comments on What’s more important, Shooting or Skiing?

The sport of biathlon combines two disciplines, shooting and cross-country skiing. That leads to the obvious question which of those two elements has the bigger effect on the overall result.


I came up with the idea to use the three statistical values which I talk about often – shooting percentage, shooting time and skiing speed – and put them into relation with the Overall World Cup rank. One way to do that is by looking at the data as a system of linear equations (a general system looks like this):

Of course the four sets of data are incompatible (i.e. the World Cup rank is a dimensionless quantity, the shooting time has a physical dimension, seconds). A way around is making all four values ranks, more precisely a ranking for each category among athletes with World Cup points. That leads to a linear system which looks something like this:

This system of linear equations is overdetermined, i.e. there are more equations than unknowns, and inconsistent, i.e. it has no solution. Luckily there are ways to finding an approximate solution, for example the method of least squares. Technically speaking, he linear system Ax = b has the approximate (least squares) solution x = (A’A)-1A’b.


After finding the least squares solution, the ratio between x1, x2 and x3 gives us the approximate influence of the shooting percentage, the shooting time and the skiing speed for an athlete’s World Cup rank.

 Men   Non-Team 
       Shooting %
          Shooting 
Time
Skiing 
          Speed %
Top 100.190.130.67
Top 200.490.010.50
Top 300.50-0.040.54
Top 400.230.060.71
Top 600.260.100.64
Top 104     0.240.070.70
Average:0.320.050.63
Influence of Shooting and Skiing on World Cup rank | Men
(0 = no effect, 1 = single factor)

Among all 104 male athletes who won World Cup points last season, the skiing speed was clearly the most important factor. The skiing speed influence on the World cup rank varied between 50 % and 71 %, depending on what group you look at.

There is the very unusual effect that for the men’s top 20 and top 30 athletes the shooting percentage briefly becomes very important, while it plays a much smaller role overall (top 104) and for the top 10. My best guess would be that that’s the region where the chart of the overall skiing pace flattens out, and therefore the shooting briefly becomes a more important factor.

 WomenNon-Team 
     Shooting %
          Shooting 
Time
Skiing 
          Speed %
Top 100.240.100.66
Top 200.290.090.62
Top 300.430.050.53
Top 400.350.060.60
Top 600.230.020.75
Top 98        0.170.020.81
Average:0.280.060.66
Influence of Shooting and Skiing on World Cup rank | Women  
(0 = no effect, 1 = single factor)

The results for the women don’t look fundamentally different. The skiing speed is slightly more important (81 %) for where an athlete is eventually ranked in the Overall World Cup. Also just like the men’s data, there is the same curious effect that the shooting percentage effect reaches its maximum for the top 30 athletes.

Some general observations:

  • The skiing pace is the most important factor for every group listed above. Overall its influence on the World Cup rank last season was about 65 % on average, pretty much across the board, both for men and women.
  • Shooting percentages play a lesser, but still significant role, with a 25-30 % influence. 
  • While shooting times have by far the smallest effect, it’s not negligible. The shooting speed accounts for about one sixth to one seventh of the total shooting influence. 

The Overall World Cup rank last season was (very roughly) determined like this: Shooting accuracy 30 %, Shooting speed 5 %, Skiing speed 65 %. Interestingly, that seems to be true for men and women alike.

Posted in Statistical analysis | Tagged shooting, skiing

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  • Introducing W. E. I. S. E: the Win Expectancy Index based on Statistical Exploration, version 1

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